Sally Beauty had a security breach in March 2014 that affected the credit and debit card accounts of thousands of customers. The company offered one free year of credit monitoring and identity-theft protection to customers who may have been affected by that incident.

A number of retailers have been hit in recent years by damaging data breaches, most notably Target Corp., when some 40 million debit and credit cards were compromised.

There has been a push by consumer rights groups and others for retailers to upgrade their security. Banks and credit card issuers are already moving in that direction.

On Tuesday, JPMorgan Chase said that it will replace all of its customers' debit cards with more secure chip-based cards nationwide and it expects to have chips on 70 percent of its debit cards by the end of 2015.